Question

there is a spinner with 15 equal areas, numbered 1 through 15. if the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 3?

Explanation:

Step1: Find multiples of 2

Multiples of 2 from 1 - 15 are 2, 4, 6, 8, 10, 12, 14. So there are 7.

Step2: Find multiples of 3

Multiples of 3 from 1 - 15 are 3, 6, 9, 12, 15. So there are 5.

Step3: Find common multiples

Common multiples of 2 and 3 (i.e., multiples of 6) are 6, 12. There are 2.

Step4: Use the inclusion - exclusion principle

The number of elements that are multiples of 2 or 3 is \(7 + 5-2=10\).

Step5: Calculate the probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{10}{15}=\frac{2}{3}\).

Answer:

\(\frac{2}{3}\)